The present work deals with the thermogasodynamic analysis of the segmented annular seal provided with Rayleigh pockets. The paper is a continuation of the work presented Arghir, M., and Mariot, A. (2017, “Theoretical Analysis of the Static Characteristics of the Carbon Segmented Seal,” ASME J. Tribol., 139(6), p. 062202.) where an isothermal model of the segmented annular seal was first presented. Each segment had three degrees-of-freedom, and its static position was obtained by solving the nonlinear equations of equilibrium. Thermal effects are now introduced by considering a simplified form of the energy equation in the thin gas film coupled with the three dimensional heat transfer in a segment of the seal and in the rotor. An efficient numerical algorithm is developed. A parametric study was performed for a segmented annular seal with pockets taken from the literature and operating with air. First, a test case proved the necessity of considering three degrees-of-freedom for the segment and not only its radial displacement. The parametric study was then performed for two different pocket depths, two pressure differences, and different rotation speeds. The results showed a non-uniform heating with larger temperatures at the leading edge of the segment where the minimal film thickness occurs. Heating is proportional to the pocket depth that lowers the lift force of the segment and to the pressure difference that closes the seal.